Maran (9:1) maintains that garments made from materials other than wool and linen require Tzitzit by force of rabbinic enactment, and not according to Torah law, whereas the Rama (ibid.) claims that the Torah obligation applies to garments made from any material.
The Mishna Berura (9:3) lists three practical differences: A)It is far more preferable to wear a Talit that requires Tzitzit according to Torah law, rather than by force of rabbinic enactment. B) If one is in doubt as to whether the Tzitzit on his Talit were spun with the required intention, and he has no other Talit, then if the Talit is made from a material requiring Tzitzit by Torah law, then he must not wear it; if the material of the Talit requires Tzitzit only by force of rabbinic enactment, then one may assume it is valid and wear it. By the same token, if one is in doubt as to whether this particular kind of garment requires Tzitzit, he must wear Tzitzit if it is of a material requiring Tzitzit by Torah law. If the material requires Tzitzit only due to Chazal's enactment, he may be lenient and wear the garment without Tzitzit. C)If a string snapped, invalidating the Tzitzit, then if the Talit requires Tzitzit according to Torah law, the individual must immediately remove it without any hesitation, even if this occurs in a public setting and he will suffer humiliation. However, if the Talit is of a material requiring Tzitzit only by force of rabbinic enactment, the concern for human dignity overrides the rabbinic decree, and he may continue wearing the garment until he leaves the public setting.
Maran (9:2) rules that woolen strings may be used as Tzitzit for garments of any material. The Bach, however, cited by the Mishna Berura (9:6), notes that other Poskim demand that the Tzitzit be made of the same material as the garment. The Bach therefore rules that one should not recite the Beracha of "Le'hit'atef Be'tzitzit" when wearing a garment with woolen Tzitzit if the garment is not also made from wool. However, the Mishna Berura observes that the prevalent Minhag (practice) is to use woolen strings for garments made from other materials without concern, and he cites several authorities who explicitly permit doing so.
Maran (9:2) rules that although in principle wool and linen strings may be used as Tzitzit for garments of any material, nevertheless, it is forbidden nowadays to use woolen strings as Tzitzit for linen garments, and vice-versa. Wearing a garment consisting of wool and linen violates the prohibition of Sha'atnez, and this prohibition is overridden by the Mitzva of Tzitzit only when the Tzitzit are made with Techelet (a special blue dye), which is required for the complete performance of the Mitzva. Since nowadays we do not make Tzitzit with Techelet (as we have lost the tradition identifying the source of the dye), and we thus cannot perform the Mitzva in its complete form, we may not wear wool and linen together. One may therefore not use wool strings for a linen garment or linen strings for a woolen garment.
Although in principle linen strings may be used as Tzitzit for garments of all materials (Maran, 9:2), the Rama (ibid.) records a view that one should not make Tzitzit from linen at all. The Mishna Berura (9:8) explains that some types of wool resemble silk, and we are therefore concerned that one might mistakenly use linen Tzitzit with a woolen garment, under the assumption that it is made from silk, and thereby violate the prohibition of Sha'atnez. Some authorities claim that this Halacha pertains only to silk garments, but garments of other materials such as cotton may have Tzitzit made from linen. The Mishna Berura rules that one may rely on this lenient position in dire situations, where no other Tzitzit are available.
Maran (9:5) records a view requiring that the garment and Tzitzit be the same color, and recommends abiding by this stringency. The Rama (ibid.), however, observes that the Ashkenazim have the practice of wearing white strings regardless of the color of the garment.